a. Explanation Definition used: Critical point: A point whose x- coordinate is the critical number c such that either f ′ ( c ) = 0 or f ′ ( c ) does not exists and y -coordinate is f ( c ) . Calculation: The given function is y = 2 3 x 3 − x 2 − 24 x − 4 . Obtain the derivative of y as follows. y ′ = 2 3 ( 3 x 2 ) − ( 2 x ) − 24 = 2 x 2 − 2 x − 24 Set y ′ ( c ) = 0 and compute the value of c b. To determine To find: The open intervals where y = 2 3 x 3 − x 2 − 24 x − 4 increases. c. To determine To find: The open intervals where function y = 2 3 x 3 − x 2 − 24 x − 4 decreases.

Finite Mathematics and Calculus with Applications

1st Edition

ISBN: 9781323188361

Author: Margaret Lial

Publisher: Pearson Education

See similar textbooks

Concept explainers

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in ter…

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which …

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the …

Videos

Question

Chapter 13.1, Problem 15E

To determine

To find: The critical numbers of the function y=23x3−x2−24x−4 .

To determine

To find: The open intervals where y=23x3−x2−24x−4 increases.

To determine

To find: The open intervals where function y=23x3−x2−24x−4 decreases.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 13.1, Problem 14E

Chapter 13.1, Problem 16E

Students have asked these similar questions

Find a plane containing the point (3, -3, 1) and the line of intersection of the planes 2x + 3y - 3z = 14 and -3x - y + z = −21. The equation of the plane is:

Determine whether the lines L₁ : F(t) = (−2, 3, −1)t + (0,2,-3) and L2 : ƒ(s) = (2, −3, 1)s + (−10, 17, -8) intersect. If they do, find the point of intersection. ● They intersect at the point They are skew lines They are parallel or equal

Answer questions 2

Chapter 13 Solutions

Finite Mathematics and Calculus with Applications

Ch. 13.1 - Find where the function is increasing and...Ch. 13.1 - Prob. 2YT Ch. 13.1 - Prob. 3YT Ch. 13.1 - Prob. 4YT Ch. 13.1 - Prob. 1WE Ch. 13.1 - Prob. 2WE Ch. 13.1 - Prob. 3WE Ch. 13.1 - Prob. 4WE Ch. 13.1 - Prob. 5WE Ch. 13.1 - Prob. 6WE

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

The critical numbers of the function y = 2 3 x 3 − x 2 − 24 x − 4 .

Solution Summary: The author explains the critical numbers of the function y=23x3.

Concept explainers

Videos

To find: The critical numbers of the function y=23x3−x2−24x−4 .

To find: The open intervals where y=23x3−x2−24x−4 increases.

To find: The open intervals where function y=23x3−x2−24x−4 decreases.

Want to see the full answer?

Chapter 13 Solutions